Question: Zoe paid $\$18.60$ in sales tax and tips for her dinner. The sales tax rate is $11\%$, and she tipped $20\%$. (The sales tax does not apply to the tip, and the tip is based on the price of the dinner before sales tax.) What was the price of Zoe's dinner, before sales tax and tip? $\$$
Solution: Since both the sales tax and the tip apply to the original price of the dinner, we can add the two rates. ${11\%}+{20\%}=C{31\%}$ To find the original price, we need to answer, ${18.60}$ is $C{31}\%$ of what number? Percent means per hundred, so $C{31\%}$ is equivalent to $C{\dfrac{31}{100}}$, which is also equal to $C{31\div100}$. $C{31\div100=0.31}$ To find the original price, we need to know $C{0.31}$ times what number equals ${18.60}$. $C{0.31}{x}={18.60}$ $\begin{aligned} C{0.31}{x}&={18.60} \\\\ \dfrac{C{0.31}{x}}{C{0.31}} &= \dfrac{{18.60}}{C{0.31}} \\\\ {x}&={60} \end{aligned}$ The price of Zoe's dinner was $\${60}$ before sales tax and tip.